Pi now at 31.4 trillion digits...

2,394 Views | 16 Replies | Last: 5 yr ago by Predmid
Caesar4
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https://appdevelopermagazine.com/pi-record-now-at-31.4-trillion-digits-in-2019-thanks-to-google-compute/
JJxvi
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I believe you mean 3.14 ten trillions of digits....
Madmarttigan
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Damn I've only memorized one trillion I'll never keep up
Formerly tv1113
Quad Dog
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Quote:

[ol]
  • Let's go to the largest size there is: the visible universe. The radius of the universe is about 46 billion light years. Now let me ask a different question: How many digits of pi would we need to calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom (the simplest atom)? The answer is that you would need 39 or 40 decimal places. If you think about how fantastically vast the universe is truly far beyond what we can conceive, and certainly far, far, far beyond what you can see with your eyes even on the darkest, most beautiful, star-filled night and think about how incredibly tiny a single atom is, you can see that we would not need to use many digits of pi to cover the entire range.
  • [/ol]
    https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/
    TexasRebel
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    Can't we just use "the next n digits of Pi" as a random number generator?
    91AggieLawyer
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    Quote:

    The radius of the universe is about 46 billion light years.

    How in the world can we even estimate this? I know math can take over from observation at some point but isn't this very assumption driven?
    TexasRebel
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    91AggieLawyer said:

    Quote:

    The radius of the universe is about 46 billion light years.

    How in the world can we even estimate this? I know math can take over from observation at some point but isn't this very assumption driven?


    It should probably be the known universe.
    ABATTBQ11
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    91AggieLawyer said:

    Quote:

    The radius of the universe is about 46 billion light years.

    How in the world can we even estimate this? I know math can take over from observation at some point but isn't this very assumption driven?


    We know the universe is expanding, so we can work backwards to when it wasn't. This means we can get an estimated age. Based on that and the speed limitations imposed by relativity, we can get a maximum diameter for the known universe. Basically, the maximum possible diameter is universal age*c.

    Beyond that, we can sort of estimate the speed and acceleration of the expansion of the universe, though these aren't universally agreed upon (pun intended). With calculus, we can take those numbers to get a better estimate than above that takes into account changes in velocity (The universe isn't expanding at a speed of c, or the speed of light).

    The most basic assumption is that there is not some kind of universe next to ours. Say our universe started from a big bang. Well, the assumption is that it was the only one in the infinite void of space, by there could have been, or might even be right now, one that is 100 billion light years away that we don't and couldn't know about. This is what that while estimate should be prefaced with "known."
    Burdizzo
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    Once in a stupor I tried to contemplate a number system based on pi, much like digital (Base-2, zeroes and ones) but with zero and pi. I then typed it into Google and found someone had already written a Wikipedia entry on the idea.

    There goes my Nobel prize for physics
    TexasRebel
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    Yep. In base-pi the circumference of a circle is 10d
    Stat Monitor Repairman
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    Allright, say they calculate it to 32 trillion and it starts repeating.

    WTF would that mean from a science and mathematics standpoint?

    Would we just say, oh cool or would it actually make a difference in anything substantive?
    TexasRebel
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    If somehow it starts repeating that means it's a mixed fraction (3 + a/b) and can be definitively calculated.

    It would no longer be irrational.
    Decay
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    Stat Monitor Repairman said:

    Allright, say they calculate it to 32 trillion and it starts repeating.

    WTF would that mean from a science and mathematics standpoint?

    Would we just say, oh cool or would it actually make a difference in anything substantive?


    Given the nature of pi, you can find any arbitrary string of digits you want, as long as you're willing to calculate out a sufficient amount of digits. So when you say "repeating", they've found many, many repeating patterns. They just don't keep repeating!
    TexasRebel
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    Repeating digits is not the same as a repeating decimal.

    22/7 is a repeating decimal

    1.101001000100001... will eventually have a run of 100 trillion zeros, but it's not repeating. The difference that is easy to see is how the number is represented as a continued fraction.
    Oyster DuPree
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    Probably getting pretty close to the end, I'd guess
    Stat Monitor Repairman
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    Im talking 3.33333 to infinity kind of repeating but with pi.
    TexasRebel
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    No. You're talking 22/7 repeating.
    Predmid
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    Stat Monitor Repairman said:

    Allright, say they calculate it to 32 trillion and it starts repeating.

    WTF would that mean from a science and mathematics standpoint?

    Would we just say, oh cool or would it actually make a difference in anything substantive?



    First off, it can't really repeat. There is a known mathematical formula to determine Pi and as it doesn't repeat. It just keeps going irrationally forever. Pi/4=1 -1/3 + 1/5 - 1/7 + 1/9 and so forth.


    And yeah, finding a repeating pattern in Pi would be cool, but have virtually zero grand implications for math & physics. Beyond ~10 to 15 digits, it has no real practical value.


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